Abstract: A new asymptotic expansion is given for a class of steady heat transfer problems of periodic composite materials. Compared to the classical form, the stronger H¹_per(Q) periodic boundary condition of auxiliary equation is replaced with 0 boundary condition. The new asymptotic expansion is still convergent to the solution of the original problem. This method is convenient for numerical computation, because the conforming element space for H¹₀(Q) is easier to be constructed than for H¹_per(Q) . On the other hand, the new asymptotic expansion solution satisfies boundary condition of the original problem, which cannot be preserved in classical method.

Key words: Homogenization, Multiscale method, Elliptic problem, Composite materials